Letters

I found something interesting that was not discussed in this discussion.

Around 480, the Chinese mathematician Zu Chongzhi gave the approximation π = 355/113, and showed that 3.1415926 < π <
3.1415927, which would stand as the most accurate value for π over the
next 900 years.

He obtained the result by approximating a circle with a 12,288 (= 211 ◊ 6) sided polygon. This was an impressive feat for the time, especially
considering that the only device he used for recording intermediate results were merely a pile of wooden sticks laid out in certain patterns.

The exact ratio of a circle's circumference to its diameter equals pi,
3.1415926535897932384626433832795...etc. In this pasuk, pi = (30/10) = 3. But the deeper reading of the text is saying: if you take 106 (the
numerical value of "kuf" "vav" - the pronounced form of "line") and replace it with 111 (the numerical value of "kuf" "vav" "hay", the written form), you have a correction factor 111/106 (or,
1.0471698113207547169811320754717). To fix up the original ration in the pasuk (30/10, 3) by multiplying by this correction factor (3*1.0471698) we get 3.14150943..., the value of pi to 4 decimal places (an error of 9 parts
in 10^-5)! It turns out that if you analyze the error in the numerator (the error in the pasuk's use of "kuf" "vav" and "hay", or 111), it turns out that this spelling yields the best approximation of pi.

Note the superfluous hei in v'kav. Perhaps it somehow alludes to taking the ratio of v'kav and v'chameish, the value of hei. If you do so, it just so happens that the ratio of the numerical values of v'chameish (355) and v'kav (113) [including one for the word itself] equals 3.14159292...which is precisely six decimal places of accuracy - one part in a million of pi's exact value, 0.00000026 more than pi, and 99.9999915...% similar to pi. It turns out that there is no better approximation for pi as a ratio of the numerical values of any two words, or of any other whole numbers less than
ten-thousand. This calculation is even internally consistent due to the fact that it is veiled within a pasuk containing the ratio of circumference to diameter.

Another thought worth noting, perhaps even stronger than the above: The ratio of the numerical values of kav with and without the hei is 111/106, 1.04716...extremely close to the correction factor (3, the circumference as
it appears in the pasuk, divided into pi), worked out as follows: pi/3 = 1.04719...Hence, due to the extra hei in kav, this pasuk comes to teach us that somehow it "knows" the drawbacks of an approximation - 3 is obviously not accurate. But for all intents and purposes, this approximation is the most succinctly accurate way to teach us the measurement of the "sea". (The Rambam writes in Peirush haMishnayos that pi at 3 is a legal definition that is the legal approximation. The reason that they can use this as the legal value of pi is the pasuk in Melochim.)

Like it or not, you are not the first one to apply gematria-based numerical tricks to the text of 1 Kings 7:23 in order to add precision to the value of Pi given therein. The only problem with all these attempts is that there is nothing in the text of that verse (nor in the classical rabbinic commentaries to it, if it matters for you) to show what exactly one has to do in order to arrive at a more precise value of Pi.
If all that you wanted were to interpret 1 Kings 7:23 in such a way as to avoid admitting that the verse contains an error, it would be much better to suggest that the figure of 10 cubits in diameter of Solomonís sea basin is an approximation (the precise value being c. 9.55 cubits), or that the diameter was measured including the width of the rims of the basin while the circumference was measured from inside the rims (which would give c. 0.225 cubits, or 11.25 cm, for the width of a single rim). Such interpretation would be less than obvious, of course, but at least it would operate with the text on its plain level, without picking gematrias at whim.
If, however, the problem which you want to solve is the acceptance of Pi = 3 in the rabbinic tradition, then no gematria-based calculations relating to the text of 1 Kings 7:23 will be of any help. There are statements in the classical rabbinic sources which take the value of Pi = 3 literally, not only in legal definitions but also in descriptions of what are supposed to be matters of fact
(see http://www.talkreason.org/articles/letter1.cfm#22).